Linear Programming in Management Accounting (Explained)

Linear programming is a management/mathematical approach to find the best outcome, giving a set of limited resources. Thousands of businesses emerge every year, as more people aim to be business owners. Most of these businesses do not experience growth and eventually fold up due to failure in management accounting.

How should businesses manage production challenges such as constraints, low productivity, and poor profit margins? What tools can companies employ to perform better?

Linear programming proves to be one of the best tools to achieve excellent results in components (decision variables), characteristics, etc., management accounting.

What is Linear Programming?

Linear programming in management accounting is a method businesses adopt to reduce costs and increase profits. In management accounting, it is used to minimize costs or maximize profits by working through various options to develop the best combination of resources.

You can only use this technique when all the relationships are linear. And even amid constraints, businesses can thrive efficiently using linear programming. By constraints, we mean the limitations that affect the financial operations of a business. These constraints can be in the form of a policy or principle that controls how a company carries out its expenditure.

Linear programming covers mathematical methods to determine how one can maximize or minimize a linear function in the face of constraints.

The application of linear programming is open  to various business/industries such as;

  • Energy
  • Food/agriculture
  • Engineering
  • Production/manufacturing
  • Transportation

Decision Variables in Linear Programming

Decision variables usually take the form of mathematical symbols ( e.g., n, x, y). These symbols represent the values that each variable(quantity) should have.

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Let’s take an example to understand decision variables better. Your business may be such that you produce two different snacks; burgers and doughnuts. It could be that people often order burgers rather than doughnuts.

Looking at your budget, you discover that you can only produce more doughnuts because the materials you need for the burgers are expensive. You have to decide where to invest more and what quantities of each snack you should produce.

You wouldn’t want to lose, would you? Remember that linear programming uses mathematical methods to achieve better output while minimizing losses and saving costs.

As a decision-maker unaware of how much quantity to produce, you can use a decision variable to create an equation. This equation will, in turn, help you determine the amounts to produce.

In this case, the variables are what quantities of burgers and doughnuts to produce and what amount of material to purchase. You can now use symbols( or decision variables) like n, x, or y to indicate the unknown quantities to get a solution faster.

Characteristics of Linear Programming

There are five major characteristics of linear programming. They include;

1. Objective Function

In a linear program, you must define the objective using a precise mathematical model. The objective is mostly to reduce costs and increase profit.

2. Constraints

A constraint restricts the level of output. The general rule is for every constraint to be described using mathematical symbols. Some examples of the constraints that may apply to a linear programming model are:

  • Shortage of funds
  • A limited amount of labor hours
  • Not enough machine time
  • A limitation in the number of materials
  • Not enough operating space
  • A constrained amount of time
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3. Non-negativity

You must write variables in positive forms only because the linear program does not support negative variables. The least is zero.

4. Linearity

As its name implies, a linear program is linear. Linear here means the proportional connection between variables (could be two or more). The proportional degree of the variables should not be more than one.

5. Finiteness

There is no room for infinite inputs/outputs in linear programming. Where various factors are unlimited, it becomes impossible to find a solution.

Advantages of Linear Programming

  • Linear programming helps in the adequate management of resources, thereby maintaining productivity.
  • As a decision-maker, linear programming equips you with tools to make the right decisions for your business.
  • The various tools linear programming provides are easy to apply to problems and bring real solutions.
  • With linear programming, you can always spot likely problems you would encounter in your business and what to do about them (e.g., during production)
  • You can also adjust to changes that would emanate in the future because the program prepares you in advance.

Disadvantages of Linear Programming

  • It is not possible to change variables.
  • You can not use the graphical method to handle problems that contain more than one variable.
  • You cannot handle functions that are not linear.
  • You may not be able to write all constraints in linear inequalities.